Download Parallel lines and transversals

PARALLEL LINES AND
TRANSVERSALS
Section 3.1
Warm Up
Identify each of the following.
1.
points that lie in the same plane
2.
two angles whose sum is 180°
3.
the intersection of two distinct intersecting lines
4.
a pair of adjacent angles whose non-common
sides are opposite rays
Parallel lines are two lines in a plane that never
intersect.
 Symbol: EF // GH
.


Skewed lines are lines in different planes that
are not parallel but will never intersect.
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A. Name all planes that are
parallel to plane WPZ.
B. Name all segments that
intersect line XQ.
C. Name all segments that are
parallel to line SR.
D. Name all segments that are
skew to line PS.
Identify each of the following.
a. a pair of parallel segments
b. a pair of skew segments
c. a pair of perpendicular segments
d. a pair of parallel planes
Line n is called the
transversal of the two parallel
lines.
 A transversal is a line that
intersects two or more lines.


When a transversal intersects
two lines, 8 angles are
formed.
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Exterior Angles: Outside //
lines.
Interior Angles: Inside // lines.
Same-Side (Consecutive)
Interior Angles: Both inside
and on the same side of
transversal.
Same-Side (Consecutive)
Exterior Angles: Both outside
and same side of transversal.
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
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Alternate Exterior Angles: Both
outside and opposite sides of
transversal.
Alternate Interior angles: (form
a Z), both inside and opposite
sides of the transversal.
Corresponding angles: (form a F)
One in and one out but on the
same side of transversal.
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
D. same-side interior angles
LINES DO NOT HAVE TO BE PARALLEL TO
FOLLOWING SPECIAL NAMES; THEY JUST DO
NOT HAVE ANY SPECIAL RELATIONSHIPS.
Give the special name for:
 ∠1, ∠ 7
 ∠ 2, ∠ 8
 ∠ 4, ∠ 6
 ∠ 1, ∠ 5
 ∠ 6, ∠ 2
 ∠ 6, ∠ 8
 ∠ 5, ∠ 8

IF THE LINES ARE PARALLEL, THEN THE 8
ANGLES FORM SPECIAL RELATIONSHIPS.
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

4 angles are acute: a, d, e, h are
congruent.
4 angles are obtuse: b, c, f, g are
congruent.
The sum of an acute and obtuse
angles equals 180 degrees.
Line a // line b
Angle
∠ 1, ∠ 5
∠ 7, ∠6
∠8, ∠ 4
∠ 3, ∠ 6
∠ 4, ∠ 6
∠ 1, ∠ 8
∠ 2, ∠ 8
Special Name
Relationship
Give the special name for:
A) ∠1, ∠8
B) ∠12, ∠14
C) ∠9, ∠16
D) ∠13, ∠16

E) ∠4, ∠1
F) ∠6, ∠8
G) ∠1, ∠5
H) 11, ∠13
Identify the transversal and classify each angle pair.
A. 1 and 3
B. 2 and 6
C. 4 and 6
Lesson Quiz: Part I
Identify each of the following.
1. a pair of parallel segments
2. a pair of skew segments
3. a pair of perpendicular segments
4. a pair of parallel planes
Lesson Quiz: Part II
Identify each of the following.
5. one pair alternate interior
angles
6. One pair corresponding angles
7. one pair alternate exterior angles
8. one pair same-side interior angles